We decompose the Backus-Smith [1993] statistic -- a low or negative correlation between relative consumption and the real exchange rate at odds with a high degree of international risk sharing -- in its dynamic components at different frequencies. Using multivariate spectral analysis techniques we show that, in most OECD countries, the dynamic correlation tends to be more negative, and significantly so, at business cycle or lower frequencies -- the appropriate frequencies for assessing the performance of international business cycle models. Theoretically, we show that the dynamic correlation predicted by standard open-economy models is the sum of two terms: a term constant across frequencies, which can be negative as a function of uninsurable risk; a term variable across frequencies, which in bond economies is necessarily positive, reflecting the insurance intertemporal trade provides against forecastable contingencies. We show that the main mechanisms proposed in the literature to account for the puzzle are consistent with the evidence.